In precision machinery processing, machine tool thermal error is the major factor to cause workpiece's error. Thus, how to control machine tool thermal error becomes essential technique to increase the processing precision and was and still is the key issue of precision machinery development ever since 1960s. The reduction of thermal error in machine tools for the purpose of processing precision and stability improvement is mostly approached by the development of a systematic logical machine tool design or a thermal error compensation method. Nevertheless, despite that the machine tool thermal error had been studied by experts all over the world for more than half a century, the affection of temperature variation upon machining precision is still very significant in modern micro-machinery industry, especially in the applications of precision molding, bio products, consumer electronics, and so on. Therefore, for precision machining process in modern industry, it is essential to have an effective and reliable technique designed for eliminating the thermal variation problem.
There are a variety of machine tools, such as machining center, precision drilling & tapping machine, sawing machine, lathe, electrical discharge machine, milling machine, grinding machine, drilling machine, tapping machine, welding/cutting machine, punching machine, bending machine, metal working machine, and the peripherals thereof. Generally, machine tools can be affected by two kinds of heat sources, which are the external heat sources and internal heat sources. The external heat sources refer to those temperature variations caused by the ambient environment or by human operations; and the internal heat sources refer to those temperature variations caused by heat generated from the machine tools' operation, which includes heat from each axial motors, the spindle, the cooling system, or movement interfaces such as the ball screw or guiding rail systems, in machine tools. Nevertheless, it doesn't matter whether the heat is from an external heat source or an internal heat source, it will be transmitted by conduction, convection, or radiation and thus changes the machine tool's thermal state. As soon as the thermal state of a machine tool is affected and changed by a heat source, it is more than possible that a certain displacement between the cutting tool tip and workpiece will be caused which is then being referred as thermal error. As noted from previous studies that there are about 40% to 70% of machining error is contributed by thermal error, thermal error is indeed the key factor for machining precision. Generally, the thermal error in machine tools is responded and handled either by means of passive compensation or by means of active suppression. In the passive compensation means, the thermal error is compensated by the calculation of a software established in a thermal error prediction model of the machine tool; and in the active suppression, the generation of the thermal error is considered in the design phase of the machine tool for minimizing or controlling the generation of thermal error. In general, comparing with the means of active suppression, the means of passive compensation is more convenient and cost effective to be put into practice. The passive compensation means had already been adopted by machine tool manufacturers, such as Mazak (Japan), Okuma (Japan), and Mikron (Swiss), etc. Therefore, the machine tool manufacturers are redirecting and focusing their long-term effort in the development of more accurate and more reliable thermal error compensation method.
There are already many studies relating to the thermal error compensation. One of which is a real-time thermal error compensation method for machine tools disclosed in “An application of real-time error compensation on a turning center”, International Journal of Machine Tools and Manufacture, 35 (12), 1995, pages 1669-1682. The method applies the information detected from the machine tool relating to temperatures, axial positions and cutting tools into an error model pre-established in the machine tool for calculating displacement prediction values and then enabling a controller of the machine tool to perform a compensation operation according to the displacement prediction values. In order to understand the thermal profile of whole machine tool, the aforesaid real-time thermal error compensation method deploys eighty thermal sensors on the machine tool for gathering temperature variation information. After analyzing the information gathered from several experiments using the eighty thermal sensors in the machine tool, the amount of thermal sensor required in any actual applications can be reduced. The aforesaid study clearly illustrates that the development of thermal error compensation technique must rely on the complete and thorough temperature variation information detected about a machine tool since it is the only way to acquire sufficient information for establishing an accurate thermal error model of the machine tool. However, since the aforesaid method requires to layout eighty thermal sensors on a machine tool, not only such large amount of thermal sensors is not easy to be deployed, but also the operation cost of the aforesaid method is increased and thus the method may not be feasible.
Another such study is a thermal error compensation device disclosed in TW Pat. No. M290082. The aforesaid thermal error compensation device for a machine tool comprises: a plurality of thermal sensors, mounted on a machine tool at positions relating to the heat sources of the machine tool; a memory card, for registering temperature information obtained by the plural thermal sensors; and a controller, configured with a macro program unit and a programmable logic control unit, for monitoring the temperature variation caused by the operations of the spindle and feed-driving system of the machine tool while performing a calculation and thus obtaining a thermal error compensation for improving the machining precision of the machine tool. It is noted that the thermal error compensation device and method claimed in the aforesaid TW patent are designed to operate similar to the previous disclosed real-time thermal error compensation method as both use signals detected from sensors on a machine tool as input to an embedded program of the machine tool for calculating thermal error compensation values. Thus, the performance of the aforesaid thermal error compensation device is highly dependent upon the completeness and thoroughness of the temperature variation information detected by sensors about a machine tool, i.e. it is highly dependent upon the layout of the plural thermal sensors. As the temperature information relating to the areas of the machine tool that are not attached by thermal sensors will not be gathered for analysis, the performance of the aforesaid device is overly rely on how much the thermal sensors are disposed on a machine tool and how those thermal sensors are distributed as well.
Yet, another such study is a control system for compensating thermal error of a machine tool disclosed in TW Pat. Pub. No. 200812746. Operationally, the control system, being adapted for controlling a machine tool, uses a software embedded in its macro program unit to gather information relating to the spindle rotation speed of the machine tool while using the gathered information as the base for calculating a compensation value, i.e. the macro program unit is enabled to use an artificial intelligent algorithm embedded therein to select a compensation equation according to the classification of the spindle rotation speed of the machine while using the selected compensation equation to obtain a compensation value. Moreover, the compensation value is resolved according to the minimum increment of the control system so as to obtain a compensation value with high resolution. With the so-obtained compensation value of high resolution, the control system is able to compensate the thermal error of the machine tool in a more precise manner as the control system is able to control the machine tool to move more precisely. It is noted that the aforesaid control system must be provided a reference database including information relating to the machine tool while its spindle is rotating at different speed and information relating to the minimum increment of the machine tool. However, the aforesaid control system is unable to response to the thermal error caused by the interaction between different internal heat sources in a machine tool as the distribution of the internal heat sources of the machine tool can be varied with the changing of feed-driving condition of the machine tool.
Yet, another such study is disclosed in U.S. Pat. No. 6,167,634, entitled “Measurement and compensation system for thermal errors in machine tools”. In the aforesaid U.S. patent, a module is provided to compensate thermal errors of the machine tool. The module comprises an operating part, a data bank, an analog to digital converter, a counter and a digital input/output part. The data bank stores in all the coefficients applied to a thermal error modeling equation which governs a relation between temperatures and thermal errors at various operating conditions. The operating part determines all the coefficients of the thermal error modeling equation which are stored in the data bank and calculates the thermal errors corresponding to the temperatures of a plurality of the thermocouples by the temperatures of a plurality of thermocouples inputted from the A/D converter and the positional coordinates of the bed inputted from the counter. Then, digital data of the calculated thermal errors are inputted into the digital input/output part and the digital input/output part converts the digital data to digital signal to input the digital signals into the controller. A controller orders the machine tool to compensate the thermal errors at the positional coordinates of the bed and the feed of the spindle. It is noted that the temperature and the error of the spindle of the machine tool is measured by the use of nine thermal sensors and five capacitance displacement transducers while the resulting measurement is provided for establishing a thermal error model. As for the measurement of the feed-driving system of the machine tool, it is detected by the use of twelve thermal sensors and a laser interferometer, and thereby, a database having information relating to machine tool operating under different feed-driving conditions can be established. Accordingly, the precision of compensation is improved by the aforesaid patent since it not only considers the thermal errors caused by different spindle speed, but also those caused under different feed-driving conditions. However, similarly to the previous-described prior arts, the precision of the compensation system in this U.S. patent still highly rely on how the thermal sensors is distributed on the machine tool, and moreover, it is not considering the affection of the machine tool's geometrical structure, the relative positions of the components in the machine tool, and the interaction between heat sources of the machine tool, and so on. Thus, the aforesaid compensation system is suitable for the machining environment similar to the experimental environment provided in this U.S. patent, so that its reliability is greatly reduced when the machining environment is different from the experimental environment.
From the above description, it is noted that the prior-art thermal compensation method comprises primarily the following three steps, which are:                (1) using thermal sensors to detect the heat sources of a machine tool while measuring the corresponding temperature variation;        (2) establishing a thermal error compensation model by the use of a statistical means while using the same to convert the detected temperature variations at different positions into thermal error compensation values; and        (3) enabling a controller to perform a thermal error compensation operation according to the thermal error compensation values.        
However, the aforesaid prior arts have the following shortcomings:                (1) lacking the physical information relating to the integral structure of a machine tool, because of that the thermal error model can not response to the affection resulting from the geometrical shape and material of the machine tool since the prior arts only use the temperature information detected from the significant nodes on the machine tool to establish its thermal error model while the greater part of the thermal error of a machine tool is resulting from the affection of temperature variation upon the integral structure of the machine tool;        (2) not considering the interaction between heat sources of a machine tool, that is because that the relative positions of the heat sources on a machine tool can be varied with the changing of feed-driving condition of the machine tool, and thus the thermal error caused by the interaction between heat sources whose positions are not fixed may be a difficult task since there may be different thermal errors even when the prior arts detect the same temperature information which can only be prevented in the prior art by a large number of experiments for achieving an optimal distribution of thermal sensors;        (3) only providing a limited amount of temperature information for the thermal error model, because of that the precision and reliability of the thermal error model can be greatly affected by the layout of the thermal sensors as the parameters required for calculating the thermal error compensation values in the thermal error model are gathered and based upon temperatures detected from those thermal sensors distributed on a machine tool, so that the more sensors used, the more precise understanding regarding to the overall temperature information of a machine tool will have, but with increasing cost;        (4) achieving a thermal error model of poor precision and reliability, which is directly consequent from the aforesaid three shortcomings.        